He is 3.
This is a hard age.
Harder than 2 years old.
4 is hard too.
Just because he is now an 'eldest' sibling... he is still, just, only, 3 years old.
MANY kids, once they become an eldest sibling... are just stressed and pressured. Because now, everyone 'expects' them (regardless of their age and development).... to 'act' older and SUDDENLY 'become' older. Even when they are not ready for that. And a kid this age doesn't even know how to be older nor even what an "eldest" sibling is. And the Eldest often becomes... the 'example' for the younger sibling, by default. And that is a LOT to carry, on the tiny shoulders of a 3 year old.
They cannot... express that.
They cannot.
The "Expectations" of the parents, upon an Eldest sibling... is often not in line, with the child's age nor cognitive or emotional development.
At this age, a child's emotions are NOT even fully developed... NOR their communication skills... NOR their social skills.... NOR do they even have, fully developed "deductive reasoning" skills, either.
They are not, fully developed yet, in all these parameters.
Thus, they act this way.
Teach him... how to communicate. Teach him how to say his feelings. Teach him it is OKAY... to have feelings. Teach him it is OKAY to feel grumpy or happy or frustrated or irked. But TEACH him, how to express that. A child is not born with inherent skills, for that. It is learned. It is taught. And it takes TIME... for a young child like this, to learn all of that.
Put it this way, not even some Adults... have those skills or abilities.
He is having to adapt, all of a sudden to a new life. "He" has a baby too. It is hard. He was an only child, all this time. He can't change what happened nor how his Mommy and family and household changed.
He is trying... he is being 3 years old. He is... fumbling as young children this age does.
Teach him how.... to cope, how to communicate, teach him the NAMES for his feelings, and how to communicate that.
Teach him... that Mommy and Daddy... ARE his soft place to fall... when he is not perfect. That he can trust you.
That he is not just at the end of punishments.
Have a 'relationship' with him... not based on performance or not.
That is what a child, this age and any age, needs.
Again, a child this age... does NOT have full development of these skills yet.
And... keep "Expectations" about him, his age.... age-appropriate.
He is 3.
Not 8.
A child this age, is not articulate yet... in MANY ways, cognitively or emotionally. Nor socially.
Don't just see the "tantrum".... SEE what is below that surface.
Below any ripple on the surface of water... there is more.
Don't see him, as just a 'tantrum.'
**Now, for a young child, being around a baby all the time and a busier Mommy... is HARD. Realize that.
They need a break too.
Maybe have him in Preschool more. 3 times a week.
My daughter was that age, when she entered Preschool and LOVED it, and I had my 2nd child (a baby then) at home. It was HER thing, HER school, HER friends, HER... routine. She needed it and even told us how she LOVES preschool and HER time.... for her.
Don't give him "techniques."
Give him... YOURSELF.
Have a "relationship"... with him.
He needs, you.
He misses, you.